Steel Design (Activate Learning wi...

Use AISC Equation E3-2 or E3-3 and determine the nominal axial compressive strength for the following cases:

a. L = 10 ft

b. L = 30 ft

To determine

(a)

Nominal compressive strength of column

Answer

1267.1kips

Explanation

Calculation:

Obtain the effective length factor for the support condition

Leff=L

Calculate the effective slenderness ratio using the formula as follows

Slenderness ratio =KLrConsider the properties of the steel from the AISC stell table Substitute 1 for k,(10×12)in for L,and 2.65 for ry.Slenderness ratio=KLr =1(10×12)2.65 =45.2

Calculate the buckling stress by using the formula as follows:

Fe=π2E(KL/r)2

substitute 29000 for E,and 45.2 for KL/r.

Fe=π2E(KL/r)2

=π2E(KL/r)2 =π2(29000)45.22 =140.1ksi

Check for slenderness ratio by using the relation as follows:

Slenderness ratio=4.71EFyFy is the yield strength.Substitute 50ksi for Fy,and 29000 for E.Slenderness ratio=4.712900050 =113.4Since the value 45.28 is less than 113.4, so caluculate critical buckling stress using the formula.Fcr=0.658(FyFe)Fy =0.658(50140.1)(50) =43.1ksi

Calculate the nominal compressive strength of column by using the formula as follows:

Calculate the effective slenderness ratio using the formula as follows

Slenderness ratio =KLrConsider the properties of the steel from the AISC steel table Substitute 1 for k,(30×12)in for L,and 2.65 for ry.Slenderness ratio=KLr =1(30×12)2.65 =135.84

Calculate the buckling stress by using the formula as follows:

Fe=π2E(KL/r)2

substitute 29000 for E,and 135.84 for KL/r.

Fe=π2E(KL/r)2

=π2E(KL/r)2 =π2(29000)135.842 =15.50ksi

Check for slenderness ratio by using the relation as follows:

Slenderness ratio=4.71EFyFy is the yield strength.Substitute 50ksi for Fy,and 29000 for E.Slenderness ratio=4.712900050 =113.4Since the value 135.84 is greater than 113.4, so caluculate critical buckling stress using the formula.Fcr=0.877Fe =0.877(15.50) =13.60ksi

Calculate the nominal compressive strength of column by using the formula as follows: